{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,11]],"date-time":"2023-10-11T06:10:20Z","timestamp":1697004620355},"reference-count":14,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":4874,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1993,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The <jats:italic>chordality<\/jats:italic> of a graph <jats:italic>G<\/jats:italic> = (<jats:italic>V, E<\/jats:italic>) is defined as the minimum <jats:italic>k<\/jats:italic> such that we can write <jats:italic>E<\/jats:italic> = <jats:italic>E<\/jats:italic><jats:sub>1<\/jats:sub> \u2229 \u2026 \u2229 <jats:italic>E<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub> with each (<jats:italic>V, E<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>) a chordal graph. We present several results bounding the value of this generalization of boxicity. Our principal result is that the chordality of a graph is at most its tree width. In particular, series\u2010parallel graphs have chordality at most 2. Potential strengthenings of this statement fail in that there are planar graphs with chordality 3 and series\u2010parallel graphs with boxicity 3. \u00a9 1993 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190170210","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T18:22:51Z","timestamp":1181240571000},"page":"221-232","source":"Crossref","is-referenced-by-count":6,"title":["On the chordality of a graph"],"prefix":"10.1002","volume":"17","author":[{"given":"Terry A.","family":"McKee","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Edward R.","family":"Scheinerman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1112\/S0025579300008500"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(74)90002-8"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01788656"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-27.1.85"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(65)90125-3"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90094-X"},{"key":"e_1_2_1_8_2","volume-title":"Algorithmic Graph Theory and Perfect Graphs","author":"Golumbic M. C.","year":"1980"},{"key":"e_1_2_1_9_2","first-page":"57","article-title":"On the structure of k\u2010trees","volume":"11","author":"Patil H. P.","year":"1986","journal-title":"J. Combinat. Inform. System. Sci."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(86)90023-4"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(74)90042-9"},{"key":"e_1_2_1_12_2","unstructured":"E. R.Scheinerman Intersection classes and multiple intersection parameters of graphs. Ph. D. thesis Princeton University Princeton NJ (1984)."},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(86)90061-4"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190020311"},{"key":"e_1_2_1_15_2","volume-title":"Matroid Theory","author":"Welsh D. J. A.","year":"1976"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190170210","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190170210","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,10]],"date-time":"2023-10-10T03:57:06Z","timestamp":1696910226000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190170210"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,6]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1993,6]]}},"alternative-id":["10.1002\/jgt.3190170210"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190170210","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,6]]}}}